High Society, The Wellcome Collection, London

This kaleidoscopic, psychedelic tour of drug use down the ages is not for the weak willed

If you have ever had a drink, or smoked a cigarette, or spent an evening watching the swirly carpet of your student room turn into a swarm of beagles, chances are you'll be itching to relive any or all of these experiences within minutes of entering this exhibition.

Being asked to think about drugs for any period of time makes you want to rush out and take a load. Which is not what you expect from a visit to the headquarters of Britain's leading charity dedicated to the improvement of public health.

No doubt the high-ups entrusted with spending the Wellcome Trust's £13bn endowment had noble intentions when, a couple of years ago, they decided to examine the history of drug-use in this wide-ranging exhibition. A kind of history of the world in a hundred crack pipes. A cynic might see the work of a marketing department that has calculated, rightly, that anything to do with drugs is guaranteed to generate plenty of media excitement. Or perhaps, a pet theory, someone came up with the brilliant pun of the title and worked back from there.

In any case, this exhibition should come with a health warning. Stay away if you're kicking a habit. Even the steeliest reformed addict will struggle not to reflect nostalgically on their own chemical experiences. How else are we expected to respond to Mustafa Hulusi's Afyon, a video installation where you immerse yourself in a darkened room surrounded by a swaying field of poppies? Pass the bong.

From the first cabinet displaying an assortment of vintage hookahs and other antique paraphernalia, we are forced to confront the fact that drugs have always had a hold over large quarters of society. We are a race of addicts, be it to coffee, qhat or cocaine. Including in their definition of a drug such benign hits as tea, the curators have raised questions about the inconsistency of attitudes and their evolution. Only this month, one study claimed that alcohol has had a more corrosive effect than heroin on public life, if you factor in socioeconomic damage with the obvious health issues.

It's a very topical subject, but the problem is not peculiar to our time: addictions have cascaded down the generations, and drugs have informed almost all cultures around the world. This comes as no great revelation. We all know the histories of the tobacco and tea trades, and even the shameful history of the opium trade – the great anti-slavery reformer Lord Palmerston propping up the British Empire by getting the Chinese hooked on dope – will be familiar to most. And you don't have to have read Thomas de Quincey's Confessions of an English Opium-Eater to guess what it's all about, though it is a treat to see the original manuscript, which normally lives, incongruously, with the rest of De Quincey's estate at Dove Cottage, Wordsworth's Cumbrian home. For High Society, it sits alongside the first draft of Coleridge's trippy voyage around Xanadu, borrowed from the British Library and looking less like a poem and more like one of those spider's webs scientists sporadically produce to prove to schoolchildren the pernicious effects of narcotics.

One exhibit illustrates perfectly how drugs can be at once glamorous and seedy. It is a 19th-century gouache illustration of Chinese opium smokers, in two parts: in one half the clients recline blissed-out in expensive clothes on a golden divan. In the other, the composition is the same, but their clothes are threadbare and patched, their couch something you would find in a Beijing squat, and their ashen faces are those of the hardened user. Bruce Alexander's 1970s video work Rat Park, an experiment which showed that rats living in a happy environment consumed less morphine than cooped-up ones, makes a similar point: drugs relieve boredom, a condition that afflicts both the very rich and the very poor – and many in between.

The danger built in to such an exhibition, as joint curator Caroline Fisher admits, is of glamorising drugs. One soft-shaded, black-and-white photo by Keith Coventry, of three women smoking crack out of adapted Diet Coke bottles, is more poetic than seedy. And anything related to the Romantic poets, and their experimentations with creative processes, will capture the youthful imagination.

The good news is that, the more you see, the more the urge to get wasted subsides. Visiting the exhibition mirrors a big night out: you charge in sober and hungry to gobble it all up, and emerge feeling just a little bit dizzy.

'High Society' (020-7611 2222), to 27 Feb